论文标题
多装饰根部森林的Hopf代数，免费匹配的Rota-Baxter代数和Gröbner-Shirshov基地
Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases
论文作者
论文摘要
随机PDE的最新进展，打字树的HOPF代数和积分方程式启发了对具有复制操作的代数结构的研究。为了理解它们的代数和组合性质，我们首先使用带有多个装饰集的根林来构建具有多个Hochschild 1 cocycle条件的自由HOPF代数。应用基础操作的代数的通用特性和Gröbner-Shirshov碱基的方法，然后在匹配的rota-baxter代数的类别中构造自由对象，这是Rota-Baxter代数的概括，使其允许多个Rota-Baxter操作员。最后，自由匹配的rota-baxter代数配备了Cocycle Hopf代数结构。
Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted forests with multiple decoration sets to construct free Hopf algebras with multiple Hochschild 1-cocycle conditions. Applying the universal property of the underlying operated algebras and the method of Gröbner-Shirshov bases, we then construct free objects in the category of matching Rota-Baxter algebras which is a generalization of Rota-Baxter algebras to allow multiple Rota-Baxter operators. Finally the free matching Rota-Baxter algebras are equipped with a cocycle Hopf algebra structure.
